Fig. 2

Graphical representation of the relationships between parameters and the data. Parameters in a black box are fixed. Parameters in a red box are marginalized out. The vector (y₁,…,y_n) is the sample, and “SD” stands for standard deviation. We denote the within-cluster phylogenies \(\left (\tau ^{(w)}_{1}, \dots, \tau ^{(w)}_{k}\right)\), k being the number of clusters, and the between-cluster phylogeny, τ^(b). Within-cluster phylogenies are degenerate when they support a cluster of size 1, while the between-cluster phylogeny is degenerate when the sample comprises only one cluster. The log-normal prior distribution for the between-cluster branch lengths is reparameterized in such a way that it has mean and standard deviation parameters, like in the normal distribution